1. Field of the Invention
This invention relates generally to power distribution methods for communications systems, and more particularly to a method of optimal power distribution in the presence of communication system crosstalk and imperfect echo cancellation.
2. Description of the Prior Art
Many communication systems rely on significant resource-sharing among multiple users, often transmission bandwidth. Proximity of different paths or channels between users can then lead to multi-user interference or crosstalk, such as the crosstalk between digital subscriber lines (DSLs) in a telephone cable or users in a wireless channel. Crosstalk lowers channel capacities and can severely limit achievable bit rates.
To achieve higher transmission speeds, a digital subscriber loop (DSL) eliminates the 3400 Hz upper bound on frequencies and uses a much broader range than the traditional voice channel. Crosstalk is a significant problem associated with high frequencies. The energy of the modulated signal radiates into adjacent copper wires in the same cable binder. Significant crosstalk is created when systems within the same cable binder, transmit information over the same range of frequencies. Crosstalk is typically categorized in one of two forms including Near End Crosstalk (NEXT) and Far End Crosstalk (FEXT). NEXT refers to interference between neighboring lines that arise when signals are transmitted in opposite directions. FEXT refers to interference between neighboring lines that arises when signals are transmitted in the same direction. FIG. 1 illustrates NEXT and FEXT between neighboring lines. NEXT, typically causes more interference, as FEXT is also attenuated as the signal propagates the length of the line.
Interference can be further subdivided into self-interference, and interference from other services. Self-interference, herein after referred to as self-NEXT and self-FEXT, refers to that which is generated by lines carrying the same service, i.e. other DSL modems carrying the same service. Interference from other sources is herein after referred to as DSIN-NEXT and DSIN-FEXT.
FIG. 2 illustrates the channel, self-NEXT and self-FEXT transfer functions, denoted by HC(f), HN(f), and HF(f), respectively, associated with an atypical DSL channel. The magnitude squared frequency response for the ith line is respectively defined as:                                                                                     H                C                            ⁡                              (                f                )                                                          2                =                  {                                                                      H                                      i                    ,                    k                                                                              if                                                                                                                                                      f                        -                                                  f                          k                                                                                                            ≤                                          W                      /                      2                                                        ,                                                                                    0                                                                                                                                            otherwise                  ;                                                              }                                    (        1        )                                                                                                H                N                            ⁡                              (                f                )                                                          2                =                              {                                                                                H                                          i                      ,                      k                                                                                        if                                                                                                                                                                      f                          -                                                      f                            k                                                                                                                      ≤                                              W                        /                        2                                                              ,                                                                                                0                                                                                                                                                              otherwise                    ;                                                                        }                    ⁢                                          ⁢          and                                    (        2        )                                                                                                                    H                  F                                ⁡                                  (                  f                  )                                                                    2                    =                      {                                                                                H                                          i                      ,                      k                                                                                        if                                                                                                                                                                      f                          -                                                      f                            k                                                                                                                      ≤                                              W                        /                        2                                                              ,                                                                                                0                                                                                                                                                              otherwise                    .                                                                        }                          ,                            (        3        )            where fk are the center frequencies of the N bins with index k ∈ {1,2, . . . , N}. The number of bins, N, is chosen such that all the channel, NEXT and FEXT transfer functions are relatively constant within each bin, such as depicted within each region 200 in FIG. 2.
Previous work at Rice University by Richard Baraniuk, Rohit Gaikwad and Nadeem Ahmed have addressed optimal power distribution for communications in the presence of crosstalk. That work considers the interference factors discussed herein above, and provides an optimal signaling spectra. The solution provided by Baraniuk et al. has an echo cancelled region and a frequency division signaling region. In the echo cancelled region, echo cancellers are used extensively to remove echo which disrupts performance. The work of Baraniuk et al. did not factor into the optimization process, the capabilities of practical echo cancellers which do not have perfect echo rejection capabilities, but instead assumed that these practical echo cancellers do have perfect echo rejection capabilities.
The problematic effects of imperfect echo cancellers can be addressed by first letting Ek denote the residual echo (after echo cancellation) as a fraction of total power in bin k. The total residual echo is then EnPn Further, the interference from other services, DSIN-NEXT, DSIN-FEXT and the additive Gaussian noise are next lumped into one noise term, N(f). Exploring the problematic effects of imperfect echo cancellers is next set forth herein after with reference to the following terms defined below wherein:
Channel capacity is conventionally defined as the maximum transmission rate (bits per second) that can be transmitted over a channel with an arbitrarily small bit-error rate (BER).
Power Spectral Density (PSD) is the distribution of signal energy over frequency. The maximum allowable PSD for a service in the presence of any interference combination is known as a PSD mask. The transmit spectrum for a service is the PSD of the transmitted signal.
In view of the foregoing, a need exists for a technique to maximize the capacity of users that are utilizing a service ‘A’; while minimizing the performance degradation of other services for an arbitrary DSL communications channel subject to 1) self-interference from other users of service ‘A’ (self-NEXT, self-FEXT), 2) interference from users of other services (DSIN-NEXT, DSIN-FEXT), 3) interference from service ‘A’ into other services, and 4) other interference including noise. NEXT, as stated above, is the dominant interference in DSL service. One simple way to eliminate self-NEXT is to use orthogonal signaling. This could be in the form of Time Division Signaling (TDS), Frequency Division Signaling (FDS), or Code Division Signaling (CDS). FDS has been shown to be the optimal signaling technique when subject to a power constraint. Self-NEXT can be eliminated using FDS, for example, by forcing upstream and downstream transmitters to use disjoint frequency bands. The resulting upstream and downstream transmissions are orthogonal and can be easily separated by their respective receivers. Moving to an FDS scheme, however, reduces the bandwidth available to each transmitter by one-half of the original bandwidth. Although FDS eliminates self-NEXT, increasing capacity, this feature is achieved at the cost of reduced bandwidth, that decreases capacity, resulting in a tradeoff. When self-NEXT is not high enough to warrant use of FDS therefore, both upstream and downstream transmitters should have the same spectrum. This is referred to as Equal PSD (EQPSD, or Echo Cancelled) signaling. The need for a technique to maximize the capacity of users that are utilizing a service ‘A’, while minimizing the performance degradation of other services for an arbitrary DSL communications channel should therefore, also take the noise environment into account when distributing power by using joint optimization techniques.